In order to obtain an insightful presentation of results for differential cross sections, we treat the raw data generated in scattering experiments or calculations and present the results in the following way.
All values of the initial kinetic energy Ei, and expressions for the scattering angle , and are in the center of mass system. Because in inelastic-collision processes the centre of mass transformation formulas require a value of the inelasticity , the most probable value of this quantity has been used.
Normally we shall plot the polar differential cross section defined by in arbitrary units against the quantity defined by , the latter by analogy with the significant reduced scattering angle for elastic-collision processes.
Experimentally, only the absolute value of the classical deflection function is meaningful, because the deflection angles and resulting from repulsive resp. attractive scattering on different sides of the target cannot be distinguished .
The reason we prefer to show deflection curves and differential cross sections on a -scale, is that for elastic scattering is in first approximation dependent only on the impact parameter b and not on the kinetic energy, and because in the collision process considered the inelastic energy is small compared to Ei.